This invention relates to optical systems employing stepped diffractive surfaces (SDSs).
More specifically, in accordance with certain of its aspects, the invention relates to the color correction of optical systems using SDSs, and, in particular, to the use of SDSs to correct axial and/or lateral chromatic aberration.
In accordance with other aspects, the invention relates to correction of monochromatic aberrations of optical systems, as well as balancing the monochromatic aberrations of non-SDS elements of an optical system against the monochromatic aberrations of SDS elements.
In accordance with additional aspects, the invention relates to correction of both chromatic and monochromatic aberrations of optical systems employing SDSs.
In accordance with still further aspects, the invention relates to:
(1) SDSs in which the surface""s step heights are determined based on the curvature of the propagating wavefront;
(2) SDSs in which the surface step widths are determined based on the shape of the base curve and the local step height;
(3) SDSs in which the surface""s step widths and step heights are determined using the grating equation (see, for example, equation (10.3) below);
(4) SDSs in which the wavefront incident on the SDS is non-planar (e.g., converging or diverging) or is planar but oriented at an angle to the optical system""s optical axis;
(5) methods for tracing rays through SDSs using the grating equation (see, for example, equation (10.3) below);
(6) methods for designing optical systems which employ SDSs;
(7) optimization of the diffraction efficiency of an SDS; and/or
(8) the use of SDSs having a radially variable step height within a diffraction order.
These latter aspects of the invention are applicable to color corrected and non-color corrected (e.g., monochromatic) optical systems.
The demand for a higher level of correction of aberrations in optical systems, preferably at a lower cost, has always exist. The modern optical designer possesses numerous design tools and techniques to correct aberrations, including aspherical surfaces, a wide variety of optical materials, diffractive optical elements, etc.
Diffractive optical elements (DOEs) have proven themselves as effective tools in the correction of aberrations of optical systems, including both monochromatic and chromatic aberrations. The advantages of a DOE come at the price of contrast reduction due to a portion of the light going into spurious diffraction orders. The efficiency of a DOE is used as the measure of the amount of light that leaks into spurious orders and causes the reduction in contrast. There are several factors that reduce the efficiency of a DOE, including manufacturing imperfections and the fundamental nature of a DOE. Improving the fabrication process can reduce the factor due to imperfections. The fundamental nature of a DOE causes reduction in efficiency due to the finite spectral band of light used in the system, as well as through xe2x80x9clight shadowingxe2x80x9d in the DOE.
One of the widely used diffractive surface configurations for a DOE is a kinoform. Kinoform DOEs have optical power and affect (change) the direction of propagation of light for the entire wavelength band and range of incidence angles. This optical power needs to be accounted for during the design stage of the optical system and affects the paraxial properties of the entire system, as well as the aberration contribution of the refractive part of the system in the case of hybrid diffractive-refractive systems. The diffraction order of a kinoform DOE in most cases is equal to unity, but can also be equal to a larger integer. The kinoform phase profile is blazed at an angle that varies as a function of aperture, i.e., as a function of radial distance from the system""s optical axis. See G. J. Swanson, Binary Optical Technology: Theoretical Limits on the Diffraction Efficiency of Multilevel Diffractive Optical Elements, MIT Lincoln Laboratory Tech. Rep. 914, 1991; D. W. Sweeney and G. E. Sommargren, Harmonic diffractive lenses, Appl. Opt., V. 34 (14), pp. 2469-2475, 1995; D. Faklis and M. Morris, Spectral properties of multiorder diffractive lenses, Appl. Opt., V. 34 (14), pp. 2462-2468, 1995; and D. Faklis and M. Morris, Polychromatic diffractive lens, U.S. Pat. No. 5,589,982, 1996.
Except for a very limited wavelength band and range of incidence angles, the diffraction efficiency (DE) of even a perfectly manufactured (theoretical) kinoform is less than unity. As a result, a certain amount of light is redistributed into diffraction orders differing from the working order, thus producing a halo in the image and a reduction in image contrast. See G. J. Swanson, 1989, supra; C. Londono and P. Clark, Modeling diffraction efficiency effects when designing hybrid diffractive lens systems, Appl. Opt., V. 31 (13), pp. 2248-2252, 1992; and G. J. Swanson, 1991, supra.
The use of DOEs, specifically, kinoform DOEs, to correct chromatic aberrations of optical systems has been discussed in detail in several articles. See T. Stone and N. George, Hybrid diffractive-refractive lenses and achromats, Appl. Opt., V. 27(14), pp. 2960-2971, 1988; M. M. Meyers and J. R. Bietry, Hybrid refractive/diffractive achromatic camera lens and camera using such, U.S. Pat., No. 5,581,405, 1996; and G. J. Swanson, Binary optics technology: the theory and design of multi-level diffractive optical elements, MIT Lincoln Laboratory Tech. Rep. 854, 1989. An ideal DOE would effectively correct the chromatism of an optical system without a significant decrease in DE.
One of the fundamental limitations on the DE of a kinoform is the xe2x80x9clight shadowingxe2x80x9d phenomenon referred to above which causes a DOE to have a duty cycle. See G. J. Swanson, 1991, supra. For a kinoform lens, the duty cycle grows with an increase in the lens"" optical power and usually increases with an increase in radial coordinate. It follows that the DE of a kinoform decreases with an increase in optical power and/or clear aperture size.
Another issue with kinoform DOEs is fabrication. See H. Welch, Fabrication Issues for DOE Design, CODE V News Supplement, Summer 1996. Because the blaze angle of the kinoform varies as a function of radial coordinate, control of this fundamental feature of a kinoform is very difficult. In many cases, the blaze profiles of kinoform DOEs are approximated with binary step profiles. See G. J. Swanson, 1989, supra; and Gary J. Swanson and Wilfrid B. Weldkamp, Diffractive optical elements for use in infrared systems, Opt. Eng., V. 28 (6), pp. 605-608, 1989. When the continuous blazed profile is approximated by 16 steps, the diffraction efficiency at the primary wavelength is reduced by about 1% from its theoretical maximum value of 100%. See Swanson and Weldkamp, supra.
The fabrication of a binary kinoform DOE typically involves lithographic projection of masks onto the surface of the DOE or a DOE master. See Swanson and Weldkamp, supra; and Gary J. Swanson and Wilfrid B. Weldkamp, Binary lenses for use at 10.6 micrometers, Opt. Eng., V. 24 (5), pp. 791-795, 1985. Such projection techniques have limitations in terms of resolution and alignment tolerances, which lead to a minimum feature size which can be fabricated without substantial loss in accuracy.
If, for example, the minimum feature size for given equipment is 2 micrometers, then for a zone width of 16 micrometers, only 8 steps (features) can be fabricated. As discussed above, 16 steps lead to a reduction in diffraction efficiency at the primary wavelength of 1%. If only 8 steps can be used, the reduction in diffraction efficiency increases to 5%. This reduction in DE means that more light is diffracted into orders other than the working order, leading to a greater contrast reduction in the image plane.
Because every step boundary implies some imperfections (e.g., due to mask alignment and/or the etching process), the binary approximation, with its increased number of boundaries, leads to increased scatter and performance deterioration (e.g., contrast deterioration) compared to a DOE having the nominal (theoretical) configuration. Another complication with kinoforms is based on the fact that the optimum depth is a function of the local zone spacing, which, in turn, is a function of radial position. See G. J. Swanson, 1991, supra. This implies a fundamental efficiency limitation for kinoforms fabricated using lithographic techniques.
The present invention avoids and/or minimizes these deficiencies of kinoform DOEs.
According to the present invention, one can correct chromatic aberrations of an optical system while introducing substantially less optical power into the system than would be introduced by a kinoform used for the same purpose. In certain cases, the power of the SDS at the primary wavelength can be zero.
Whereas the reduction in DE due to the finite spectral band of light is unavoidable for any DOE, as discussed in detail below, the structure of the diffractive component according to the present invention can be optimized such that the reduction of DE due to variable incidence angle (finite field of the optical system and/or wavefront curvature of the incident light) is minimized. More generally, the present invention provides an optimally shaped DOE (substrate shape as well as microstructure) such that the surface has a maximum DE in the working order.
With regard to the xe2x80x9clight shadowingxe2x80x9d phenomenon, a DOE according to the present invention has almost no xe2x80x9cbendingxe2x80x9d effect on the rays, so that the light shadowing of the surface is, in general, negligible. In certain cases, the light shadowing is completely eliminated, the duty cycle is zero, and the DE is constant across the radial coordinate of the SDS and has its maximum theoretical value of unity.
In the case when the wavefront incident on the DOE according to the present invention is not planar, or when the DOE has nonzero axial power, for example when the efficiency is optimized for a finite field (see below), the duty cycle for the light propagating through the DOE is not zero and the DE is less than one. However, because the power of the DOE according to the present invention is substantially less than that of a kinoform employed for the same purpose, the duty cycle of the DOEs of the invention are always less than that of a kinoform, and the DE at the primary wavelength is always higher.
These properties of the DOE of the present invention make it the preferred choice, compared to a kinoform, in applications that demand the highest contrast (highest DE).
As to manufacturability, whereas kinoforms have a variable blaze angle across the aperture (see G. J. Swanson, 1991, supra), DOEs according to present invention have planar steps orthogonal to the DOE""s axis of symmetry. Compared to a kinoform there is one degree of freedom less to control, so that fabrication of a DOE according to the present invention using single point diamond turning equipment is more accurate compared to a kinoform. Also the microstructure of the DOE of the present invention is inherently composed of steps, thus eliminating the problems caused by a binary approximation to the non-step like blaze of a kinoform.
In sum, essentially any aberration corrective optical function, which can be performed by a kinoform, can also be performed by a DOE according to the present invention, but will typically have better efficiency and will be easier to make.
In view of the foregoing, it is an object of the invention to provide correction of chromatic aberrations, monochromatic aberrations, or both chromatic and monochromatic aberrations in optical systems by means of one or more stepped diffractive surfaces which are used alone or in combination with other approaches for correcting such aberrations.
It is a further object of the invention to provide aberration-corrected optical systems, which have at least one SDS and the aberrations introduced by the SDS are balanced against the aberrations of the rest of the system.
It is another object of the invention to provide aberration-corrected optical systems which have (1) a finite (i.e. nonzero) field of view and (2) at least one SDS, wherein the monochromatic performance of the system with the SDS is substantially equal to and, preferably, is better than the system""s monochromatic performance without the SDS.
It is a further object of the invention to provide optical systems, which employ at least one SDS and have optimized diffraction efficiencies.
It is an additional object of the invention to provide improved methods for incorporating SDSs in computerized processes for designing lens systems.
FIGS. 1A and 1B illustrate optical elements employing stepped diffractive surfaces 13a and 13b of the type with which the present invention is concerned. To simplify these drawings, opposing surfaces 15a and 15b of these elements have been shown as planar. In the general case, the opposing surfaces can have optical power or can be another stepped diffractive surface, if desired.
As shown in these figures, the stepped diffractive surfaces 13 comprise a plurality of concentric planar zones 17 (also referred to as xe2x80x9cstepsxe2x80x9d) which are orthogonal to optical axis 19. The zones lie on a base curve which is shown as part of a circle in FIGS. 1A and 1B, but in the general case can be any curve of the type used in optical design, including conics, polynomial aspheres, etc. The base curve may also constitute a base surface in cases where the concentric planar zones are not axially symmetric, i.e., where their widths are a function of xcex8 in an (r, xcex8, z) cylindrical coordinate system having its z-axis located along the system""s optical axis. For ease of reference, the phrase xe2x80x9cbase curvexe2x80x9d will be used herein and in the claims to include both the axially symmetric and axially non-symmetric cases, it being understood that in the non-symmetric case, the base curve is, in fact, a base surface. In either case, the base curve can be characterized by a vertex radius which can be used in calculating the paraxial properties of the stepped diffractive surface.
The stepped diffractive surfaces of the invention are distinguished from digitized (binary) kinoforms by the fact that the sag of the stepped diffractive surface changes monotonically as the zone number increases. The sag of the microstructure of a binary kinoform, on the other hand, always exhibits a reversal in direction at some, and usually at many, locations on the surface. This is so even if the base curve for the binary kinoform has monotonic sag.
Quantitatively, the zones of the stepped diffractive surface preferably have widths (wi) and depths (di) which satisfy some or all of the following relationships:
|di| |di+1| less than 2.0, for i=1 to Nxe2x88x922;xe2x80x83xe2x80x83(A) 
|di|≅jixcex0/|(n2xe2x88x92n1)|, for i=1 to Nxe2x88x921;xe2x80x83xe2x80x83(B) 
wi/xcex0 greater than 1.0, for i=1 to N;xe2x80x83xe2x80x83(C) 
where xe2x80x9cjixe2x80x9d is the order of the ith zone of the stepped diffractive surface (jixe2x89xa71), N is the total number of zones (N=6 in FIGS. 1A and 1B), xcex0 is the primary or nominal wavelength of the optical system, and xe2x80x9cn1xe2x80x9d and xe2x80x9cn2xe2x80x9d are the indices of refraction of the media on either side of the stepped diffractive surface, with light traveling through the stepped diffractive surface from the n1 medium to the n2 medium The step xe2x80x9cdepthxe2x80x9d is also referred to herein as the step xe2x80x9cheight.xe2x80x9d
The xe2x80x9cjixe2x80x9d nomenclature is used in the above equations to indicate that the working order of the stepped diffractive surface can be different for different zones. In many cases, the same working order will be used for all zones; however, for manufacturing reasons, it may be desirable to use different working orders for some zones, e.g., if the zone width wi would become too small for accurate replication with a constant working order, especially, for a constant working order of 1. In this regard, it should be noted that ji can be made greater than 1 for all zones, again to facilitate manufacture of the stepped diffractive surface by, for example, reducing the overall number of zones comprising the surface and, at the same time, increasing the depth and width of the individual steps. For simplicity of presentation and in view of the lack of a universal convention for identifying orders in diffractive systems, the xe2x80x9cjixe2x80x9d values are assumed to be positive numbers, it being understood that they could equally well be negative numbers.
Like the monotonic sag characteristic, the |di| |di+1| less than 2.0 characteristic distinguishes the diffractive surfaces of the invention from digitized (binary) kinoforms, where |di| |di+1| is normally greater than 2.0 for at least some steps, i.e., where the kinoform profile returns to the base curve. The |di|≅jixcex0/|(n2xe2x88x92n1)| characteristic in combination with the requirement that jixe2x89xa71 also distinguish the stepped diffractive surfaces of the invention from digitized kinoforms in that this expression calls for an optical path difference for each step of at least jixcex0 while for a digitized kinoform of the same diffractive order the optical path difference for each step is at most jixcex0/2 in the case of a two level digitization and becomes even smaller for the digitizations actually used in practice, e.g., an eight or sixteen level digitization. The wi/xcex0 greater than 1.0 characteristic affects the efficiency of the stepped diffractive surface, with larger ratios generally corresponding to greater efficiencies. In addition, this ratio needs to be sufficiently large for scalar theory to apply. See G. J. Swanson, Binary Optics Technology: Theoretical Limits on the Diffraction Efficiency of Multilevel Diffractive Optical Elements, Massachusetts Institute of Technology Lincoln Laboratory Technical Report 914, Mar. 1, 1991, p.24.
It should be noted that when a stepped diffractive surface is incorporated in an optical element as illustrated in FIGS. 1A and 1B, the optical material making up the element could have an index of refraction greater than or less than the surrounding medium. Also, light can pass from left to right or from right to left through the element. Thus, for a stepped diffractive surface, which transmits light, four cases are possible:
(1) passage from a higher index of refraction medium to a lower index of refraction medium through a concave stepped diffractive surface;
(2) passage from a lower index of refraction medium to a higher index of refraction medium through a concave stepped diffractive surface;
(3) passage from a higher index of refraction medium to a lower index of refraction medium through a convex stepped diffractive surface; and
(4) passage from a lower index of refraction medium to a higher index of refraction medium through a convex stepped diffractive surface.
As further variations, rather than transmitting light, the stepped diffractive surface 13 can be reflective, in which case equation (B) above becomes:
|di|≅jixcex0/2n, for i=1 to Nxe2x88x921xe2x80x83xe2x80x83(Bxe2x80x2) 
where xe2x80x9cnxe2x80x9d is the index of refraction of the medium in which the light travels before contacting the reflective surface.
Combinations of the foregoing cases can, of course, be used in optical systems that employ the invention.
For some applications of the invention, N is small and for others, it is large. For example, N can be greater than 175 and can even be greater than 200 or more. Similarly, for some applications, small sags are needed while for others, the sag needs to be large. For example, the sag can be greater than 0.25 millimeters or even greater than 0.30 millimeters or more.
Similarly, for some applications of the invention, the optical system has a finite (non-zero) semi-field of view, while for others it does not. For example, the operative semi-field of view can be greater than 5xc2x0, or even greater than 10xc2x0, 20xc2x0, 40xc2x0, or more.
In accordance with one of its aspects, the invention provides an optical system having an optical axis and comprising:
(A) at least one refractive or reflective optical surface having a non-zero optical power; and
(B) at least one stepped diffractive surface which has a clear aperture, and within said clear aperture comprises N concentric planar zones orthogonal to the system""s optical axis which define a base curve, said zones satisfying the relationship:
di/di+1 less than 2.0, for i=1 to Nxe2x88x922, 
where di is the magnitude of the displacement along the optical axis between zone i and zone i+1;
wherein:
(i) removal of the stepped diffractive surface and its replacement with a surface having the same optical power results in an increase in the system""s monochromatic aberrations, i.e., its measured and/or calculated monochromatic aberrations (e.g., its calculated blur size), including, for example, astigmatism, coma, distortion, spherical aberration, etc., and/or a change in the system""s focal plane position.
As used herein, a surface having the same optical power "PHgr" as an SDS is a spherical surface that has a radius R defined as: R=(n2xe2x88x92n1)/"PHgr", where n2 and n1 are the refractive indices on either side of the surface. The optical power of the SDS is evaluated at xcex0. When the SDS power is zero (SDS has no power), then the surface that has the same optical power is a plane (R=∞).
The optical system also exhibits characteristic (i) when the stepped diffractive surface is removed and replaced with a non-stepped surface having the SDS""s base curve.
In accordance with another aspect, the invention provides an optical system for forming an image of an object, said system having an optical axis and a non-zero operative semi-field of view in the direction of the object and/or a non-zero operative semi-field of view in the direction of the image, said system comprising:
(A) at least one refractive or reflective optical surface having a non-zero optical power; and
(B) at least one stepped diffractive surface positioned away from the stop of the optical system and which has a clear aperture, and within said clear aperture comprises N concentric planar zones orthogonal to the system""s optical axis which define a base curve, said zones satisfying the relationship:
di/di+1 less than 2.0, for i=1 to Nxe2x88x922, 
where di is the magnitude of the displacement along the optical axis between zone i and zone i+1;
wherein
(i) removal of the stepped diffractive surface and its replacement with a refractive surface having the same power results in an increase in at least one of the system""s longitudinal or lateral chromatic aberrations, i.e., its measured and/or calculated longitudinal and/or lateral chromatic aberrations.
The optical system also exhibits characteristic (i) when the stepped diffractive surface is removed and replaced with a non-stepped surface having the SDS""s base curve.
In accordance with a further aspect, the invention provides an optical system for forming an image of an object, said system having an optical axis and an operative semi-field of view in the direction of the object and/or an operative semi-field of view in the direction of the image, said system comprising:
(A) at least one refractive or reflective optical surface having a non-zero optical power; and
(B) at least one stepped diffractive surface which has a clear aperture and within said clear aperture comprises N concentric planar zones orthogonal to the system""s optical axis which define a base curve, said zones satisfying the relationship:
di/di+1 less than 2.0, for i=1 to Nxe2x88x922, 
where di is the magnitude of the displacement along the optical axis between zone i and zone i+1;
wherein:
(i) removal of the stepped diffractive surface and its replacement with a refractive surface having the same power results in:
(a) an increase in at least one of the system""s chromatic aberrations; and
(b) an increase in the system""s monochromatic aberrations within the system""s operative semi-field of view in the direction of the object when that operative semi-field of view is largest, or the image when that operative semi-field of view is largest, or both the object and the image when the operative semi-fields of view in those directions are equal.
Alternatively, the optical system exhibits characteristics (a) and (b) when the stepped diffractive surface is removed and replaced with a non-stepped surface having the SDS""s base curve.
In accordance with an additional aspect, the invention provides an optical system, said system having an optical axis and an operative wavelength range which has a minimum wavelength xcexmin, a maximum wavelength xcexmax, and a primary or nominal wavelength xcex0 which lies between xcexmin and xcexmax, said system comprising:
(A) at least one refractive or reflective optical surface having a non-zero optical power; and
(B) at least one stepped diffractive surface which has a clear aperture and within said clear aperture comprises N concentric planar zones orthogonal to the system""s optical axis which define a base curve, said zones satisfying the relationship:
di/di+1 less than 2.0, for i=1 to Nxe2x88x922, 
where di is the magnitude of the displacement along the optical axis between zone i and zone i+1;
wherein di varies as a function of distance from the optical axis and the system has an on-axis diffraction efficiency (calculated or measured) at xcex0 which exceeds the system""s on-axis diffractive efficiency (calculated or measured) at xcex0 when di is constant across the SDS""s clear aperture and is equal to mxcex0/|n1xe2x88x92n2| where m is an integer and n1 and n2, as defined above, are the indices of refraction on either side of the stepped diffractive surface.
In accordance with another aspect, the invention provides an optical system for forming an image of an object, said system having an optical axis, an operative semi-field of view in the direction of the image, and an operative wavelength range which has a minimum wavelength xcexmin, a maximum wavelength xcexmax, and a primary or nominal wavelength xcex0 which lies between xcexmin and xcexmax, said system comprising:
(A) at least one refractive or reflective optical surface having a non-zero optical power; and
(B) at least one stepped diffractive surface which has a clear aperture and within said clear aperture comprises N concentric planar zones orthogonal to the system""s optical axis which define a base curve, said zones satisfying the relationship:
di/di+1 less than 2.0, for i=1 to Nxe2x88x922, 
where di is the magnitude of the displacement along the optical axis between zone i and zone i+1;
wherein the system has an average diffraction efficiency (calculated or measured) over the operative semi-field of view in the direction of the image at xcex0 which is equal to or greater than the system""s average diffractive efficiency (calculated or measured) over the operative semi-field of view in the direction of the image at any other wavelength between xcexmin and xcexmax.
As described in detail below, to achieve such maximization of the average diffraction efficiency, the step depth di is selected to be different from that which the prior art teaches should be used for xcex0, e.g., for the case of a stepped diffractive surface at an interface between air and a material of refractive index n, the step depth is selected to be different from mxcex0/(nxe2x88x921), where m is an integer. This choice of step depth, in turn, results in maximum diffraction efficiency for xcex=xcex0 at an off-axis point rather than on-axis. In other words, on-axis diffraction efficiency is sacrificed to achieve maximum average diffraction efficiency, an approach to the diffraction efficiency problem which has not previously been used in the art.
In accordance with another aspect, the invention provides a method for providing axial and/or lateral color correction for an existing lens system which comprises a plurality of existing lens elements, said method comprising:
(a) adding an element having a stepped diffractive surface to an existing lens system;
(b) adjusting the overall length of the optical system (i.e., the distance between the system""s first and last optical surfaces) to accommodate an element with an SDS; and
(c) defining the position of the SDS within the optical system so that the axial and/or lateral color of the system is reduced or corrected
wherein the number of existing lens elements and their radii of curvature and composition are not changed.
In accordance with still further aspects, the invention provides:
(1) A method for reducing at least one aberration of an optical system which comprises (i) a stepped diffractive surface (SDS) and (ii) an optical surface which has optical power and is not a stepped diffractive surface (non-SDS), said method comprising:
(a) tracing rays through the system by representing the SDS by an equation which describes diffraction by a grating; and
(b) using the rays traced in step (a) to select one or more parameters of the system which reduce said at least one aberration.
(2) A method for reducing at least one aberration of an optical system which comprises at least one optical element, said method comprising:
(a) incorporating an additional optical element in the system which comprises a stepped diffractive surface (SDS); and
(b) selecting the spacing between the SDS and the at least one optical element;
wherein step (b) is performed by tracing rays through the system by representing the SDS by an equation which describes diffraction by a grating.
(3) An optical system comprising:
(a) a stepped diffractive surface (SDS); and
(b) an optical surface which has optical power and is not an SDS (non-SDS);
wherein the SDS makes an optically significant contribution to the correction of the optical system""s lateral color.
(4) An optical system comprising:
(a) a stepped diffractive surface (SDS); and
(b) an optical surface which has optical power and is not an SDS (non-SDS);
wherein the SDS makes an optically significant contribution to the correction of the optical system""s astigmatism.
(5) An optical system comprising:
(a) a stepped diffractive surface (SDS); and
(b) an optical surface which has optical power and is not an SDS (non-SDS);
wherein the SDS makes an optically significant contribution to the correction of the optical system""s coma.
(6) An optical system comprising:
(a) a stepped diffractive surface (SDS); and
(b) an optical surface which has optical power and is not an SDS (non-SDS);
wherein the SDS makes an optically significant contribution to the correction of the optical system""s distortion.
(7) An optical system comprising:
(a) a stepped diffractive surface (SDS); and
(b) an optical surface which has optical power and is not an SDS (non-SDS);
wherein the SDS makes an optically significant contribution to the correction of the optical system""s spherical aberration.
(8) An optical system comprising:
(a) a stepped diffractive surface (SDS); and
(b) an optical surface which has optical power and is not an SDS (non-SDS);
wherein the SDS makes optically significant contributions to the correction of two of the optical system""s aberrations.
(9) An optical system comprising:
(a) a stepped diffractive surface (SDS); and
(b) an optical surface which has optical power and is not an SDS (non-SDS);
wherein:
(1) the optical system has a field of view and a nominal wavelength xcex0; and
(2) the SDS has a constant step height selected to increase the SDS""s average diffraction efficiency over the field of view at xcex0.
(10) An optical system comprising:
(a) a stepped diffractive surface (SDS); and
(b) an optical surface which has optical power and is not an SDS (non-SDS);
wherein:
(1) the optical system has a field of view and a nominal wavelength xcex0; and
(2) the SDS has a constant step height selected so that the maximum diffraction efficiency at xcex0 occurs at an intermediate field point within the field of view.
(11) An optical system comprising:
(a) a stepped diffractive surface (SDS); and
(b) an optical surface which has optical power and is not an SDS (non-SDS);
wherein the diffraction efficiency of the SDS is optimized for a wavefront incident on the SDS which is non-planar.
(12) An optical system comprising:
(a) a stepped diffractive surface (SDS); and
(b) an optical surface which has optical power and is not an SDS (non-SDS);
wherein the optical system has an optical axis and the diffraction efficiency of the SDS is optimized for a planar wavefront which, at the SDS, has a direction of propagation which is oriented at a non-zero angle to said axis.
(13) An optical system comprising:
(a) a stepped diffractive surface (SDS); and
(b) an optical surface which has optical power and is not an SDS (non-SDS);
wherein the diffraction efficiency of the SDS is optimized over a spectral range.
(14) A stepped diffractive surface comprising a plurality of steps having a plurality of step heights wherein the step heights are not all equal within a diffraction order.
(15) A stepped diffractive surface comprising a base curve and a plurality of steps having a plurality of step heights wherein the base curve is an asphere and the step heights are not all equal within a diffraction order.
In connection with aspects (1) through (8) above, the SDS""s contribution to the aberration(s) is preferably substantially balanced against the non-SDS""s contribution to the aberration(s).
In the foregoing, the aberrations (monochromatic and/or chromatic) and the diffraction efficiencies can be calculated or measured. Also, as used herein, the phrase an xe2x80x9coptically significant contributionxe2x80x9d means that the contribution is to be evaluated in terms of the specifications and/or performance of the optical system. Thus, an optically significant contribution can be a very small contribution for a system which has stringent specifications and/or a high level of performance, e.g., a diffraction limited system. On the other hand, an optically significant contribution may need to be a large contribution for a system which has lenient specifications and/or a low level of performance. Persons skilled in the art can readily determine whether a contribution is optically significant or not for any particular application of the invention in accordance with their general experience in determining whether a contribution is of concern in terms of meeting desired specifications or performance criteria. The phrase xe2x80x9csubstantially balancedxe2x80x9d means that the residual aberration resulting from the combination of the SDS""s contribution to the aberration and the non-SDS""s contribution to the aberration is not optically significant.
In accordance with an additional aspect, the invention provides methods for designing and producing optical systems which substantially satisfy predetermined specifications and which include at least one stepped diffractive surface comprising:
(a) defining the stepped diffractive surface as a function of step heights di and the shape of the base curve;
(b) performing a ray trace through the optical system;
(c) defining the system""s aberrations;
(d) optimizing the system, including the step heights di and the shape of the base curve, based on the system""s predetermined specifications.
In accordance with a further aspect, the invention provides methods for designing and producing optical systems which substantially satisfy predetermined specifications and which include at least one stepped diffractive surface comprising:
(a) defining the stepped diffractive surface as a function of step heights di and step widths wi;
(b) performing a ray trace through the optical system;
(c) defining the system""s aberrations;
(d) optimizing the system, including the step heights di and step widths wi, based on the system""s predetermined specifications.
Optical systems designed in accordance with either or both of the foregoing aspects of the invention can be produced using a variety of lens fabrication and assembly procedures well known in the art. The invention, of course, can also be practiced using fabrication and assembly procedures, which may be developed in the future. General discussions of applicable manufacturing techniques can be found in, for example, The Handbook of Plastic Optics, 2nd edition, U.S. Precision Lens Inc., Cincinnati, Ohio, 1983, and Horne, Douglas F., Optical Production Technology, 2nd ed., Adam Hilger, Ltd., Bristol, 1983, the relevant portions of which are incorporated herein by reference.
The stepped diffractive surface(s) used in connection with the foregoing aspects and embodiments of the invention can be made using a variety of techniques now known or subsequently developed. Examples of such techniques including machining of individual elements using, for example, a diamond turning machine or, more preferably, producing a master mold and forming elements having the desired diffractive surface using injection molding techniques. Elements having stepped diffractive surfaces, especially when made by molding, will generally be composed of a plastic material, e.g., an acrylic polymer, although other materials, e.g., glass materials, can be used if desired.
In addition to the foregoing, the invention also provides computer programs which embody the methods of the invention for designing optical systems which include an SDS. The programs can be embodied as an article of manufacture comprising a computer usable medium, such as a magnetic disc, an optical disc, or the like, upon which the program is encoded. The optical design data generated by the programs can similarly be stored on various types of storage media for distribution and or display (e.g., display as an image of the optical design either on paper or on a computer monitor).
These method-of-designing aspects of the invention are practiced on a digital computer system configured by suitable programming to perform the various computational steps. The computer system can comprise a general purpose scientific computer and its associated peripherals. The system should include means for inputting data and means for outputting the results of the design process both in electronic and visual form. The output can also be stored on a disk drive, tape drive, or the like for further analysis and/or subsequent display.
The earliest reference discussing the use of a stepped diffractive surface in an optical system is A. I. Tudorovskii, xe2x80x9cAn Objective with a Phase Plate,xe2x80x9d Optics and Spectroscopy, Vol. 6(2), pp. 126-133 (February 1959). The optical system considered by Tudorovskii was a telescope objective and the stepped diffractive surface was designed to correct the system""s secondary color, as opposed to its primary color.
Significantly, with regard to the present invention, the Tudorovskii article deals with an optical system which has essentially a zero angular field of view. Also, in Tudorovskii, the wavefront at the SDS surface is planar and orthogonal to the system""s optical axis. The maximum SDS base curve sag in the Tudorovskii examples does not exceed 0.012 mm. That is equivalent to an optical path difference (OPD) of 10 waves or 0.006 mm.
Tudorovskii provides no disclosure with regard to balancing the monochromatic aberrations of SDSs against the monochromatic aberrations of non-stepped optical surfaces, no disclosure with regard to correcting lateral chromatic aberrations of an optical system with an SDS, no disclosure with regard to treatment of individual steps in the process of designing a lens system which includes an SDS, no disclosure of the use of the grating equation to determine the optical properties of an SDS, no disclosure of methods for optimizing the diffraction efficiency of an SDS, and no disclosure of an SDS having a variable step height within a diffraction order.
U.S. Pat. No. 5,153,778, which issued to Jose M. Sasian-Alvarado in 1992, also discloses a stepped diffractive surface. The Sasian-Alvarado system is monochromatic and the stepped diffractive surface is said to be useful for correcting field curvature and/or spherical aberration. The patent suggests use of a quadratic base curve to correct field curvature and a quartic base curve to correct spherical aberration.
With regard to the present invention, this patent does not mention correction of chromatic aberrations, axial or lateral, and does not include any disclosure of techniques for incorporating a color-correcting, stepped diffractive surface in a lens system. The patent does not mention correction of other monochromatic aberrations in addition to the ones listed above. Similarly, the patent has no disclosure with regard to the treatment of individual steps in the process of designing a lens system which includes an SDS, no disclosure of the use of the grating equation combined with the shape of the base curve to define a ray trace through an SDS, and no disclosure of methods for optimizing the diffraction efficiency of an SDS and, in particular, no disclosure of the use of variable step heights for that purpose. Significantly, the disclosure of this patent is entirely qualitative and does not include a single prescription for an SDS or any other components of an optical system.
In 1993, Jose M. Sasian-Alvarado and Russell A. Chipman published an article on stepped diffractive surfaces entitled xe2x80x9cStaircase lens: a binary and diffractive field curvature corrector,xe2x80x9d Applied Optics, Vol. 32, No. 1, Jan. 1, 1993, pages 60-66 (the xe2x80x9cSasian/Chipman articlexe2x80x9d). In the article, the SDS is analyzed based on fourth order wave aberrations and the Sweatt model is used to perform the ray trace. (See W. C. Sweatt, Describing Holographic Optical Elements As Lenses, JOSA, V. 67, pp. 803-808, 1977; W. C. Sweatt, Mathematical Equivalence Between A Holographic Optical Element And An Ultra-High Index Lens, JOSA, V. 69, pp. 486-487, 1979.)
The fourth order aberration theory cannot substitute for an actual (real) ray trace and provides only an approximation. The Sweatt model can be used to trace rays through a general diffraction surface, but this model is not shape preserving and does not constrain the steps to be orthogonal to the optical axis. The concept of the optical power of a surface is used in optical design to calculate the paraxial properties of the optical system. When the optical power of the refractive substrate and the Sweatt model for the diffractive properties of an SDS are combined, the solution will have no paraxial power. Only a few steps in close proximity to the optical axis will retain the properties of a SDS, i.e., will have step surfaces perpendicular to the optical axis. To compensate for the local curvature of the substrate in the non-paraxial domain, the steps are not constrained to be perpendicular to the optical axis, i.e., they will constitute a kinoform rather than an SDS. As a result, the Sweatt model cannot be used to balance the monochromatic aberrations of a SDS against the monochromatic aberrations of non-stepped optical surfaces in an optical system based on an actual ray-trace.
In its Section 2(D), the Sasian/Chipman article discusses the use of an SDS to correct field curvature. In this example, the refractive lens and the stop position were chosen to correct coma and astigmatism and the SDS was located at the stop to correct field curvature. The example, however, does not account for other monochromatic aberrations introduced by the SDS, including astigmatism, coma and spherical aberration. Although the article does not include sufficient information to determine quantitatively the extent of correction of the field curvature in the above example, it is clear that there is no teaching on how the monochromatic aberrations of the SDS should be balanced against the monochromatic aberrations of other system components.
Placement of the SDS at the stop in this example means that the SDS can have no effect on the lateral color of the system. Accordingly, it is clear that Sasian/Chipman did not recognize the usefulness of SDSs in correcting this aberration. Similarly, Sasian/Chipman does not disclose or suggest SDSs having deep sags or high numbers of zones within the SDS""s clear aperture. The maximum base curve sag of the SDS described in the Sasian/Chipman article does not exceed 0.192 mm, which corresponds to 150 steps and a maximum OPD of 150 wavelengths or 0.095 mm. Significantly, in use, the Sasian/Chipman SDS has a clear aperture defined by the stop of the system which is equal to 10 millimeters. This clear aperture corresponds to just 58 steps, an OPD of just 58 wavelengths, and a sag of just 0.075 millimeters.
Although primarily concerned with field curvature correction, the Sasian/Chipman article does mention the effects of a stepped diffractive surface on longitudinal chromatic aberration. In particular, the article discusses using an acrylic element having an SDS with a concave base curve on one surface and a plane on the other to correct the longitudinal chromatic aberration of a plano-convex lens composed of BK7 glass and having a focal length of 100 mm. The stepped diffractive surface is described as being located 58 mm behind the BK7 lens and as having a base curvature of 166.5 mm. It is thus located in a converging beam. (See Section 3(B) of the Sasian/Chipman article.)
Using the techniques of the present invention, calculations were performed for the combination of a plano-convex BK7 lens and a plane parallel plate made from acrylic. In particular, calculations were performed assuming that this combination was corrected for spherical aberration, i.e., assuming that at the primary wavelength of xcex0=0.588xcexc, the convex surface of the BK7 lens had a radius of curvature of xe2x88x9251.68 mm and a conic constant of xe2x88x922.2947. This combination was found to have an RMS spot radius of 0.05 microns which is less than the system""s Airy disk radius of 2.6 microns, i.e., the original system was diffraction limited.
Replacement of a planar surface of the plate by an SDS element was found to introduce sizable spherical aberration into the system at the above mentioned primary wavelength since the SDS is in a converging wavefront. In particular, the RMS spot radius and the geometrical spot radius for the system at 0.588 microns were found to be 5.3 microns and 9.6 microns, respectively, while the Airy disk radius, as discussed above, was only 2.6 microns, i.e., the system employing an SDS was not diffraction limited at the primary wavelength.
Plainly, the Sasian/Chipman article does not disclose or suggest simultaneously correcting chromatic aberrations and balancing the monochromatic aberrations of an SDS against monochromatic aberrations of a system""s non-stepped optical surfaces. If aberration balancing had been performed, the monochromatic performance of the refractive portion of the system would show monochromatic aberrations, including spherical aberration, of the opposite sign to that introduced by the SDS. The Sasian/Chipman article neither discloses nor suggests such xe2x80x9copposite signxe2x80x9d balancing.
U.S. Pat. No. 5,629,799, which issued to Maruyama et al. in 1997, as well as U.S. Pat. Nos. 5,796,520 and 5,883,774, which issued to Maruyama in 1998 and 1999, respectively, are devoted to using an SDS for correcting the axial color as well as spherochromatism of an optical system. At column 40, lines 17-20, of U.S. Pat. No. 5,629,799 caution is expressed against using hybrid diffractive lenses (i.e., lenses composed of a diffractive plastic element affixed to a glass element) in systems having a wide field of view. In particular, in discussing the types of systems other than those illustrated in their patent in which such hybrid lenses might be used, Maruyama et al. wrote: xe2x80x9cIt should be noted . . . that the hybrid lens is also applicable to other types of optical system unless the view angle is very wide.xe2x80x9d
The only example of the above patents which has a semi-field of view greater than 5xc2x0 is Example 5E, the structure of which is shown in Maruyama""s FIG. 72 and the prescriptions for which are set forth in Maruyama""s Tables 6E and 7E. In particular, Table 6E sets forth the original catadioptric lens system of this example, and Table 7E sets forth the prescription for the SDS which is to replace surface 4 of the original prescription in order to provide axial color correction.
The original lens system without an SDS is well-corrected on-axis and at the same time has significant residual field aberrations. Using the prescription of Table 6E and conventional ray-tracing techniques, an RMS spot size radius of 0.84 microns (1.29 microns geometric radius) was determined for the original system at a primary wavelength of 0.5876 microns (the d-line of Maruyama""s FIG. 73). This spot size is less than the system""s Airy disk radius of 4.7 microns, i.e., the monochromatic performance of the original system is diffraction limited on-axis.
Using the techniques of the present invention, the RMS spot size radius on-axis of the system at the same wavelength with surface 4 replaced with the SDS defined by Table 7E was found to be 9.8 microns. That is, the RMS spot size increased more than ten-fold upon introduction of the SDS and was now more than twice the Airy disk radius of 4.7 microns.
Thus, with regard to on-axis monochromatic aberrations, introducing an SDS changed a well-corrected, diffraction limited system into one which can not be considered as diffraction limited. Because the level of correction of the off-axis aberrations was low, the contribution of the off-axis aberrations introduced by the SDS into the system was significantly less than the system""s residual off-axis aberrations such that the level of correction of the off-axis aberrations was practically unchanged.
Plainly, this example of Maruyama et al. does not teach balancing the monochromatic aberrations of an SDS against monochromatic aberrations of a system""s non-stepped surfaces. Rather, the example demonstrates that in correcting chromatic aberrations, an SDS can cause great harm to monochromatic performance unless the techniques of the present invention are employed.
For comparison, original surface 4 was also replaced with a plane. This modification of the system was found to degrade the system""s monochromatic performance at the primary wavelength to essentially the same extent as the replacement of surface 4 with the SDS defined by Table 7E.
In addition to Example 5E, the above patents employ stepped diffractive surfaces in Examples 2, 2B, 3B, 5B, 3D, 4D, and 1E through 4E. Using the techniques of the present invention, it was determined that the SDSs of Examples 2B, 3B, 5B, 4D, and 1E have practically no effect on on-axis spherical aberration so that the monochromatic spot size is essentially unchanged when the SDS is replaced by a planar surface located at the SDS""s vertex. For each of these examples, the SDS is located in collimated light parallel to the optical axis. Examples 2E through 4E in which the SDS is oriented at an angle with respect to the system""s optical axis were not analyzed but are expected to behave similarly to Example 1E. All of the above examples have finite fields and substantial residual off-axis aberrations. Maximum base curve sag of the SDS in these examples does not exceed 0.158 mm (Example 4D, FIG. 57), which is equivalent to an OPD of 140 waves or 0.082 mm.
For Examples 2 and 3D, where the SDS was located in converging light, it was determined that the SDS introduces sizeable spherical aberration into the system and the RMS spot size decreases when the SDS is replaced with a plane located at the vertex of the SDS. That is, the SDS makes the monochromatic performance of the system at the reference wavelength worse, not better. Thus, once again, these examples illustrate the inability of the prior art to balance an SDS""s monochromatic aberrations against monochromatic aberrations of non-stepped optical surfaces in the system. (In analyzing Example 2, it was assumed that the best imagery was located on axis in accordance with Maruyama et al.""s FIG. 6.)
As discussed above and in more detail below, in accordance with certain of its aspects, the present invention employs stepped diffractive surfaces in which the step height varies within a diffraction order. In connection with Example 3D, the Maruyama patents discuss decreasing step height by xe2x80x9cabout 1%xe2x80x9d to provide equal xe2x80x9cphase differencesxe2x80x9d for the central and peripheral annular segments of a high numerical aperture lens. (Maruyama et al. ""799 patent at column 37, lines 36-58.)
Significantly, Maruyama et al. give no information regarding which annular segments should be considered central and which should be considered peripheral. Accordingly, there is no way of knowing from this reference where the decrease in step height should begin. Moreover, the reference does not teach whether all peripheral step heights should be decreased by the same amount or whether some should be decreased more than others. In the end, Maruyama et al. teach away from varying the step height and use a constant step height for Example 3D: xe2x80x9c[T]he discontinuity in phase that occurs if the difference in thickness between annular segments is made equal in the whole part of the lens will cause no problem in practical applications. Therefore, in Example 3D under discussion, xcex94N is expressed as a linear function of N and the difference in thickness between individual annular segments is set to be equal in both the central and peripheral parts of the lens.xe2x80x9d (Maruyama et al. ""799 patent at column 37, lines 51-58.)
In the above mentioned patents, the lateral color introduced by the SDS is ignored. It is believed by Maruyama et al. that an SDS corrector can be placed xe2x80x9cany distancexe2x80x9d from the lens with the field of view ranging from 1.4 degrees to 1.7 degrees (see Table 5B from example 2B, Table 7B from example 3B, and Table 13B from example 5B). In fact, as can be shown using the ray trace techniques of the present application, displacement of the SDS from the lenses shown in the above examples will introduce lateral color and the lateral color can exceed other aberrations of the system, making the performance of the system unacceptable.
The optical systems with which the present invention is concerned are typically those which comprise one or more elements which together have a non-zero optical power. Because the index of refraction of optical materials varies with wavelength, such systems exhibit chromatic aberrations, both axial and lateral, and much effort has been expended in developing techniques for dealing with these aberrations.
Axial chromatic aberration is an aperture dependent aberration. It manifests itself as a change in focus position along a system""s optical axis with a change in wavelength. For an optical system designed to have an operative wavelength range which extends from a minimum wavelength xcexmin to a maximum wavelength xcexmax, the system""s axial chromatic aberration can be quantified by calculating (or measuring) the system""s shortest and longest focal points within the operative wavelength range and then calculating (or measuring) the distance along the optical axis between those calculated (or measured) focal points.
This calculated (or measured) distance will be referred to herein as the xe2x80x9coptical system""s axial chromatic aberration or, more simply, as the xe2x80x9caxial color,xe2x80x9d and one of the objects of the invention is to hold this parameter within the design specifications (performance requirements) of the optical system.
Depending on its shape, an SDS may exhibit axial color having a sign (direction) opposite to that of the optical system to be corrected. The one or more stepped diffractive surfaces can be the sole means for correcting axial chromatic aberration or can be combined with other techniques, e.g., the stepped diffractive surface(s) can be combined with one or more color-correcting doublets or kinoform diffractive lenses and their binary counterparts.
When calculated focal points are used to evaluate the chromatic aberration parameter, such focal points are obtained from: (1) measured or prescription values for the optical elements of the system; (2) measured or modeled values for the indices of refraction of the optical elements as a function of wavelength; and (3) a lens design computer program, such as the program sold by Focus Software Incorporated, Tucson, Ariz., under the trademark ZEMAX, the program sold by Optical Research Associates, Pasadena, Calif., under the trademark CODE V, or other commercial or non-commercial programs having similar capabilities. When the system includes a stepped diffractive surface, the techniques disclosed below for incorporating such a surface in the lens design process are used in determining the system""s axial chromatic aberration.
When measured values are used, such values can be obtained using, for example, an optical bench.
As discussed above, most of the prior disclosures of SDSs related to correction of axial color.
Lateral chromatic aberration, or lateral color, is a chromatic difference of magnification of an optical system. It is a field dependent aberration and manifests itself as a change in height of the chief ray at the image plane with a change in wavelength. Since it is a field-dependent aberration, lateral color has an insignificant effect in systems with small fields of view. At the same time, lateral color can play a detrimental role in systems with finite fields.
For an optical system designed to have an operative wavelength range which extends from a minimum wavelength xcexmin to a maximum wavelength xcexmax, the system""s primary lateral chromatic aberration can be quantified for a given field by calculating (or measuring) the highest and the lowest intersection points of a chief ray with the image plane for wavelengths within the operative wavelength range and then calculating (or measuring) the distance between those points in that plane.
This calculated (or measured) distance will be referred to herein as the xe2x80x9coptical system""s lateral color for a wavelength range from xcexmin to xcexmaxxe2x80x9d or, more simply, as the xe2x80x9clateral colorxe2x80x9d. One of the objects of the invention is to hold this parameter within the design specifications (performance requirements) of the optical system by means of one or more stepped diffractive surfaces.
In accordance with the invention, it has been determined that an SDS placed away from an optical system""s aperture stop introduces lateral color into the system. The amount of lateral color introduced by the SDS is dependent on the shape and position of the SDS in the optical system. Since the SDS introduces lateral color into an optical system, it can be used to correct lateral color produced by other components (surfaces) in the system. The one or more stepped diffractive surfaces can be the sole means for correcting lateral color or can be combined with other techniques, e.g., the stepped diffractive surface(s) can be used in combination with appropriate selection of materials for the refractive components in the system, or with diffractive kinoform lenses and their binary counterparts.
Correction of the lateral color of the optical system should not compromise the system""s performance with regard to axial color. An optical element that affects lateral color will also introduce changes in the axial color of the system. This means that when SDS is used to correct the lateral color of the optical system, the SDS""s effect on axial color must also be taken into account in the design of the system. In optical systems with extended fields, the correction of chromatic aberrations usually requires the correction of both axial and lateral chromatic aberrations, making that task much more difficult compared to optical systems with small fields of view, where only the axial chromatic aberration needs to be accounted for and corrected.
As in the evaluation of axial color, when calculated intersection points are used to evaluate lateral color, such points are obtained from: (1) measured or prescription values for the optical elements of the system; (2) measured or modeled values for the indices of refraction of the optical elements as a function of wavelength; and (3) a lens design computer program, such as the program sold by Focus Software Incorporated, Tucson, Ariz., under the trademark ZEMAX, the program sold by Optical Research Associates, Pasadena, Calif., under the trademark CODE V, or other commercial or non-commercial programs having similar capabilities. When the system includes a stepped diffractive surface, the techniques disclosed below for incorporating such a surface in the lens design process are used in determining the system""s lateral chromatic aberration.
Again as in the case of the axial color, when measured values are used, such values can be obtained using an optical bench.
As discussed above, there were no suggestions in the prior art regarding using an SDS to correct the lateral color of an optical system. Rather, the lateral color introduced by an SDS was totally ignored. In particular, in U.S. Pat. Nos. 5,629,799, 5,796,520 and 5,883,774 do not in any way take into account the lateral color introduced by the SDSs disclosed in those patents.
Chromatic aberrations are, of course, only a few of many aberrations that can affect the performance of an optical system. Monochromatic aberrations are at least as important as chromatic aberrations. Most of the monochromatic aberrations are aperture dependent and some of them are also field dependent. In particular, as is well known in the art, the primary monochromatic aberrations other than spherical aberration, i.e., coma, astigmatism, field curvature, and distortion, as well as the lateral chromatic aberration discussed above, are field dependent aberrations. These aberrations become more difficult to correct as the field of view increases.
The effects of system aberrations (chromatic and/or monochromatic) can be evaluated using a variety of computation (and measurement) techniques known in the art. Representative examples of the techniques include, but are not limited to, computing the spot size (also known as blur spot size), modulation transfer function (MTF), Strehl ratio, wave aberrations, and edge response function. The above techniques can be used for the evaluation of both monochromatic and polychromatic performance of the optical system. The polychromatic system performance is computed based on the weighted performance average at several wavelengths within the operative wavelength range of the system. The measure of monochromatic aberrations is evaluated at least at a representative (primary) wavelength xcex0 within the system""s operative wavelength range (also referred to as the xe2x80x9creference wavelengthxe2x80x9d or the xe2x80x9cnominal wavelengthxe2x80x9d). The selected wavelength may be the system""s central wavelength (i.e., xcex0=(xcexmin+xcexmax)/2), but can be a different wavelength depending upon the design criteria for the system.
In the examples presented below, the level of correction of monochromatic aberrations is assessed in most cases using a computed geometric blur spot size. It is to be understood that the use of this measure is for purposes of illustration only and is not intended to limit the invention in any way. As will be evident to persons skilled in the art, other measures of monochromatic aberrations now known or subsequently developed can equally be used in the practice of the invention.
In the case when the level of aberration correction of the original optical system is low, the aberrations introduced by an SDS may not substantially affect the image quality of the system. On the other hand, for systems with a high level of aberration correction, even a small amount of aberrations introduced by an SDS can play a detrimental role in system performance. It is the relative contribution of the aberrations of the SDS to the total aberrational budget of the optical system that affects the performance of the optical system.
In accordance with the invention, it has been determined that the aberrations introduced by an SDS into an optical system are in general proportional to the sag of the SDS substrate, the curvature of the incident wavefront, and the operative semi-field of view of the system.
Prior discussions of the use of SDSs in optical systems were concerned with the correction of only a limited subset of the aberrations actually introduced by an SDS. The discussions were limited primarily to the correction of aperture dependent aberrations, such as axial color, spherical aberration and spherochromatism, even in systems with finite, i.e. nonzero, fields where SDSs, in fact, introduce a variety of field dependent aberrations. For the cases where correction of a field dependent aberration was discussed, i.e., field curvature in the Sasian patent and the Sasian/Chipman article, correction of the rest of the aberrations introduced by the SDS, including other field dependent monochromatic aberrations and chromatic aberrations, was not done. Introduction of an SDS into an optical system with a finite field of view (FOV) will unavoidably affect the field aberrations of the optical system, including the field curvature, astigmatism, coma and higher order aberrations, and, unless placed at the stop location, will affect the lateral color. Correction only of the field curvature in a system with a finite FOV does not assure adequate system performance. It is believed that the prior art""s inability to account for the actual aberrations introduced into an optical system by an SDS was due to the lack of techniques for real ray tracing through optical systems containing an SDS. As a result, the prior art could not accurately determine the optical effects, including monochromatic effects and effects on lateral color, of an SDS in an optical system.
Most of the prior art discussions were also limited to the case when the SDS was placed in a collimated beam so that the wavefront of light at the primary wavelength propagating through the SDS is planar. In the few cases of a nonplanar wavefront, it was erroneously believed that the SDS would have no effect on the aberrations of the optical system (see the Maruyama patents).
In sum, the prior art limited itself to optical systems where there was at least one of the following conditions: (1) field dependent aberrations were neglected, corresponding to systems with practically zero FOV; (2) not more than two aberrations from several introduced by the SDS were considered; (3) the stepped diffractive surface was employed at the stop location and the wavefront incident on the SDS was planar and was directed along the system""s optical axis; (4) the effects of the wavefront curvature at the primary wavelength propagating through the SDS on monochromatic performance of the optical system were neglected; and/or (5) the overall monochromatic performance of the system was relatively poor, so that the aberrations introduced by the SDS were substantially smaller than the aberrations of the initial system. Under these conditions, it was apparently believed that an SDS could be analyzed qualitatively, e.g., through the use of wavefront graphs with phase delays, or semi-quantitatively, e.g., through the use of the Sweatt model. Nowhere in the prior art is there any disclosure of a lens design process in which the dimensions of the individual steps of an SDS, their actual heights and widths, are taken into account.
In particular, there is no disclosure in the prior art where all real ray aberrations introduced by an SDS into an optical system, as opposed to just a limited number of aberrations, has been accounted for in the design process and balanced against the aberrations of the rest of the system. Balancing the aberrations of an SDS means that the performance of the optical system will deteriorate and its aberrations will increase when the SDS is replaced by the equivalent optical power refractive surface. In many cases that equivalent optical power refractive surface is a plane, but it may be refractive surface with optical power when the SDS has optical power at the reference wavelength. There also is no disclosure in the prior art where the SDS is positioned away from the stop of the optical system in order to correct the lateral chromatic aberration of the system. Nowhere in the prior art is there any disclosure of the real ray aberrations, chromatic and monochromatic, introduced into an optical system due to the wavefront incident on the SDS being not planar and/or at an angle to the optical axis of the system.
Significantly, as revealed by the present invention, the locations of the individual steps of an SDS (their heights and widths) are important for evaluation of the real ray aberrations of the SDS. For the general case, by incorporating the locations of the individual steps in the lens design process, SDSs can be effectively employed in essentially any optical system, including systems which have significant fields of view, non-planar wavefronts, and/or excellent correction of monochromatic and chromatic aberrations. This represents an important advance in the art since it allows the full aberration-correcting potential of stepped diffractive surfaces to be achieved.
It is clear that in any optical system employing an SDS all aberrations should be considered, including the monochromatic and chromatic aberrations. In a properly designed optical system, the aberrations of an SDS should be accounted for and balanced with/against the aberrations of the rest of the system. As discussed below, in certain of its aspects, the present invention employs one or more stepped diffractive surfaces (SDSs) to achieve color correction (balancing) of an optical system and, at the same time, balances the monochromatic aberrations of the SDS against monochromatic aberrations of non-stepped optical surfaces in the system. This combination of correction (balancing) of chromatic aberrations and balancing of monochromatic aberrations in an optical system employing an SDS has not previously been taught or achieved in the art.
Beginning with Tudorovskii and continuing through to Maruyama et al., prior discussions of SDSs have assumed that such surfaces can be understood in terms of their effects on the phase relationship between different parts of a wavefront. As Tudorovskii stated in 1959: xe2x80x9cThe plate formed by joining together cylindrical rings separates light rays parallel to the axis into cylindrical bundles and imparts to them different phases without changing their direction . . . xe2x80x9d; xe2x80x9cThe introduction of the phase plate PP does not change the geometrical path of the rays, but divides the spherical surface QQ into spherical zones with different phases . . . xe2x80x9d; and xe2x80x9cA phase plate, computed for a wavelength xcex0 and located . . . in a parallel beam of the same wavelength xcex0, does not influence the image of an infinitely remote point . . . xe2x80x9d (Tudorovskii at pages 171, 172, and 174, respectively; emphasis added.)
Following this line of reasoning, the Sasian patent, the Sasian/Chipman article, and the Maruyama patents each include a figure which shows a planar wavefront remaining planar after passing through or being reflected by an SDS. See, for example, FIG. 3 of the Sasian patent (U.S. Pat. No. 5,153,778), FIG. 2 of the Sasian/Chipman article, and FIG. 60 the Maruyama patents. The step height of the SDS was chosen by the prior art to be: di=jixcex0/|(n2xe2x88x92n1)|.
It was not realized by the prior art that:
(a) It is the grating equation (see (10.3) below) that governs the ray propagation through an SDS and affects the system aberrations. That is, an SDS can be considered as a grating with a variable step spacing (or width wi) placed on a non-planar substrate defined by the shape of the base curve and the blaze angle of the grating is constrained to maintain the planar step boundaries perpendicular to the optical axis.
(b) The specific step heights of an SDS are important primarily only for distributing the light between the different orders of diffraction, i.e., they primarily affect only the diffraction efficiency (DE). Instead of taking into account (a) and (b), the prior art used the phase shift reasoning exemplified by the above-referenced figures of the Sasian patent, the Sasian/Chipman article, and the Maruyama patents. This reasoning does not allow one to reach any meaningful conclusions regarding propagation through an SDS. Moreover, in the Sasian patent, it led to wrongful conclusions regarding wavefront curvature, i.e., it led to the conclusion than an on-axis planar wavefront will remain planar after interaction with an SDS regardless of the widths of the zones making up the SDS. The fundamental problem with the phase shift reasoning is that it does not provide real ray-tracing of an optical system.
Under the phase shift reasoning, an SDS of constant step height illuminated with a planar wavefront, i.e., collimated light which is parallel to the optical axis, will not produce monochromatic aberrations at the reference wavelength. In accordance with the present invention, it has been determined that this existing conception of the effects of an SDS on a planar wavefront is incorrect. In fact, an SDS of constant step height introduces monochromatic aberrations at the reference wavelength, specifically, spherical aberration, into a planar wavefront propagating along the optical axis. That is, spherical aberration depends on the zone width wi and/or the base curve shape of the SDS.
In contrast to the phase shift reasoning of the prior art, the present invention treats an SDS as a grating with a groove width wi, which is a function of radial distance from the optical axis, placed on a non-planar substrate defined by the base curve. The blaze angle of the grating is constrained in such a manner that the bounding surfaces of the microstructure are perpendicular to the optical axis. The groove spacing of the grating affects the direction of rays propagating through the SDS. The height of the SDS steps affects the efficiency of light propagating into different diffractive orders and does not substantially affect the direction of rays or the wavefront propagating through the SDS. For a given step height hi and shape of the SDS base curve, the radial spacing wi is uniquely defined. This, in turn, defines the direction of light propagating through the SDS. Changing the base curve of the substrate without changing the heights of the steps changes the groove spacing, causing a change in the wavefront (direction of rays) of light propagating through the SDS. This was not understood in the prior art.
As shown below, a planar wavefront propagating along the optical axis through an SDS with a spherical substrate and a constant step height defined by equation (B) above exhibits spherical aberration at the primary wavelength. This spherical aberration is proportional to the sag of the SDS substrate and increases with an increase of the SDS""s maximum clear aperture and the curvature of the base curve. To illustrate this consider a singlet 20 with focal length of 100 mm made from acrylic and having a planar entrance surface 21 and a refractive exit surface 22, as illustrated in FIG. 2A. Surface 22 has optical power and is characterized by a radius xe2x88x9249.1668 mm and conic constant xe2x88x922.2251. During the calculations, the nominal wavelength was chosen to be 0.588 microns, corresponding to an SDS step height of 1.195 microns. The light impinging on the entrance surface 21 of the singlet was assumed to be at the reference wavelength, collimated and parallel to the optical axis. The shape of surface 22 of the singlet was chosen such that the spherical aberration of the singlet at the nominal wavelength was completely corrected, making the singlet diffraction limited.
Replacing the plane surface 21 by an SDS introduces spherical aberration into the system. When the radius of curvature of the SDS is large and the aperture is small, the amount of spherical aberration produced by the SDS is insignificant. For example, when the SDS has a radius of curvature of xe2x88x92845 mm and an aperture size of 20 mm, the amount of spherical aberration is negligible and the singlet remains diffraction limited. The situation, however, changes with a reduction of the SDS radius and/or an increase in clear aperture.
FIGS. 2B and 2C are ray fan plots showing the spherical aberration produced by the singlet as the characteristics of the SDS are changed. OBJ represents the object size in millimeters, EY and EX represent the tangential and sagittal directions in the image plane, and PY and PX represent the tangential and sagittal directions in the pupil of the system. The scales of FIGS. 2B and FIG. 2C are +/xe2x88x9210 microns and +/xe2x88x925 microns, respectively.
In the case corresponding to FIG. 2B, the SDS""s base curve had a radius xe2x88x9250 mm and the aperture remained 20 mm. In FIG. 2C, the SDS""s base curve had a radius xe2x88x92845 mm and the aperture was increased to 168.5 mm. In each case the focal length of the singlet remained at 100 mm. The spherical aberration introduced by the SDS was 6.3 microns and 3.6 microns for the two cases, respectively, whereas the radius of the Airy disk was 3.6 microns and 0.7 microns, respectively. These SDSs clearly made the singlet not diffraction limited.
As can be seen from this basic example, a planar wavefront propagating parallel to the optical axis through an SDS with a constant step height and a spherical base curve does exhibit spherical aberration at the reference wavelength, an effect not previously recognized in the art, and that aberration can severely reduce the performance of the optical system. That aberration shows up at relatively high apertures and/or high curvatures of the SDS base surface.
As shown below, an SDS introduces even more severe aberrations when the propagating wavefront is not planar and/or is propagating at an angle to the optical axis.
In view of these considerations, it is clear that an SDS cannot simply be treated as a phase element, as incorrectly believed in the prior art. An SDS is a diffractive element, and it has diffractive effects governed by the grating equation, which lead to monochromatic aberrations at the reference wavelength.
In another basic case, when a planar wavefront is propagating at an angle to the optical axis of an SDS with a spherical base curve and a constant step height, several field dependent aberrations are introduced, including field curvature, astigmatism and coma. FIG. 3 illustrate these effects. In FIG. 3A, numeral 31 denotes an SDS with base curve radius of 166.5 mm positioned at a stop having a radius of 5 mm. This figure thus corresponds to the example of the Sasian/Chipman article. Numeral 32 denotes an xe2x80x9cidealxe2x80x9d lens, i.e., a mathematical model of a thin lens that has optical power and no aberrations. Numeral 33 denotes the image plane. The traced rays correspond to a wavelength of 0.6328 microns and to two field positions: on-axis field and a 30xc2x0 field. The position of the image plane is adjusted to bring the tangential ray bundle for 300 field in focus.
FIG. 3B shows the ray aberration curves corresponding to this case, where OBJ represents the object field angle in degrees, EY and EX represent the tangential and sagittal directions in the image plan, and PY and PX represent the tangential and sagittal directions in the pupil of the system. The scale for FIG. 3B is +/xe2x88x92100 microns. As can be seen in this figure, the SDS introduces both astigmatism and coma into the system.
An SDS introduces an even wider variety of aberrations when the incident wavefront is not collimated and/or a finite spectral band is considered.
As discussed above, the magnitude of the monochromatic aberrations introduced by an SDS at the reference wavelength depends on the SDS""s clear aperture and the curvature of its base curve. An increase in either or both of these factors leads to an increase in the sag of the SDS base curve. The base curve sag can be used as a qualitative measure of aberrations introduced by an SDS. The magnitude of monochromatic aberrations also depends on the field angle and the wavefront curvature of propagating light, as well as the microstructure geometry of the SDS. It is this important discovery which forms the basis of the present invention""s improvements on the prior uses of SDSs in optical systems.
The computed base curve sags of the SDSs of FIGS. 2B and 2C were 1.0 mm and 4.2 mm, respectively, which corresponds to OPDs of 846 waves or 0.497 mm and 3524 waves or 2.072 mm, respectively. The highest base curve sag value for an SDS employed in the prior art was calculated to be 0.192 mm in the Sasian/Chipman article (OPD of 150 wavelengths or 0.095 mm). However, in use, Sasian/Chipman located their stop at the SDS and limited the aperture to 10 mm so that the effective sag was only 0.075 mm. As shown above (see FIG. 3B), even this small amount of sag results in a significant amount of off-axis aberrations at a 30xc2x0 field.
In accordance with one aspect of the invention, the monochromatic aberrations shown in FIG. 2 can be effectively reduced by making the SDS""s base curve aspherical. As set forth above, the geometric spot size radius for the singlet of FIG. 2B with a spherical base curve was 6.3 microns (RMS spot size radius of 3.0 microns) while the Airy disk radius was 3.6 microns, i.e., the system is not diffraction limited. By aspherising the base curve by using a conic constant of xe2x88x9250, the geometric and RMS spot size radii are reduced to 0.5 and 0.3 microns, respectively, i.e., with this change, the monochromatic aberrations are reduced to a level that makes the system diffraction limited. Similarly, for FIG. 2C, the geometric and RMS spot size radii for a spherical base curve are 3.6 microns and 1.6 microns, respectively, while the Airy disk radius for this case is 0.7 microns. Thus, as for the FIG. 2B example, for a spherical base curve, the system is not diffraction limited. By employing a base curve having a conic constant of xe2x88x92600, the geometric and RMS spot size radii are reduced to 0.07 and 0.04 microns, respectively. With this change, the spherical aberration is substantially smaller than the diffraction blur attributable to the lens"" aperture (Airy disk radius is 0.7 microns) and the system is considered to be diffraction limited.
Although a conic constant has been used to introduce asphericity into the base curve, it is to be understood that other mathematical formulations can be used for this purpose, including polynomial aspheres, splines, etc. It should be noted that for the case when the SDS step height is constant and the impinging wavefront is planar there always exists some residual spherical aberration and by aspherizing the base curve the spherical aberration introduced by an SDS is reduced to an acceptable level but not completely eliminated.
The Maruyama patents discussed above employ aspherical base curves in some of their SDS examples. This asphericity, however, is not used to eliminate monochromatic aberrations (spherical aberration in particular) at the reference (primary) wavelength, but rather was intended to correct spherochromatism introduced into the system at wavelengths other than the reference (primary) wavelength. As discussed above, the Maruyama patents, as well as the rest of the prior art, worked under the assumption that an SDS with a spherical base curve and a constant step height when illuminated with a planar wavefront does not exhibit monochromatic aberrations at the reference wavelength, an assumption which the present invention, with its method of preserving the normal-to-the-axis-orientation of individual steps through the use of the grating equation to analyze an SDS, shows was wrong.
In summary, the prior art considered an SDS as a phase-shifting structure that divides the incoming wavefront into several individual portions and introduces optical path differences that are multiples of the nominal wavelength. The fact that it is diffraction that governs light propagation through the system and that the grating equation should be used to perform a real ray-trace was neither disclosed nor recognized in the art. The optical path difference between the individual portions of the wavefront is important to achieve a certain level of diffraction efficiency for an SDS at a given wavelength, but is not sufficient to permit an SDS to be incorporated in practical, real world optical systems. Moreover, the prior art thought that to obtain the maximum diffraction efficiency an SDS with a constant step height should be employed. It was not realized that to obtain the highest DE the step height may need to be made a function of the incident wavefront curvature and/or field angle.
As is well known in the art, optical systems which employ diffractive elements can suffer from low diffraction efficiency as a result of substantial amounts of light being diffracted into orders other than the design order for the system. None of the prior uses of stepped diffractive surfaces have specifically addressed this problem and none have provided techniques for optimizing the diffraction efficiency of optical systems employing such surfaces. As discussed below, in certain embodiments, the present invention addresses and solves this problem by intentionally sacrificing on-axis diffraction efficiency in order to maximize average diffraction efficiency. In other embodiments, the diffraction efficiency at the nominal wavelength xcex0 is maximized by selecting a step height different from the value suggested in the prior art of di=jixcex0/|n2xe2x88x92n1|.